Exam P topic · 23–30% syllabus weight

Exam P General Probability practice problems

Independently written solutions mapped to this official syllabus topic. Pages appear only after all required checks agree.

Topic orientation

What this topic tests

General Probability connects event algebra, conditional probability, independence, counting, and Bayes’ theorem. The main work is usually translating a verbal experiment into events whose intersections and complements can be calculated cleanly.

Exam questions often hide the decisive denominator or conditioning event inside the setup. A strong solution names the event first, checks that the pieces form a valid probability model, and only then substitutes numbers.

Typical failure modes

  • Using an unconditional probability where a conditional denominator is required
  • Treating mutually exclusive events as independent
  • Forgetting a complement or double-counting overlapping cases

Published ledger

Exam P General Probability practice problems and solutions

Each entry shows its independent calculation record and links to the official source without reproducing protected wording.

  1. SOA Exam P Sample Question #1Inclusion–ExclusionVerified
  2. SOA Exam P Sample Question #2Inclusion–ExclusionVerified
  3. SOA Exam P Sample Question #3Inclusion–ExclusionVerified
  4. SOA Exam P Sample Question #4IndependenceVerified
  5. SOA Exam P Sample Question #5Inclusion–ExclusionVerified
  6. SOA Exam P Sample Question #6Conditional ProbabilityVerified
  7. SOA Exam P Sample Question #7Expected ValueVerified
  8. SOA Exam P Sample Question #8Inclusion–ExclusionVerified
  9. SOA Exam P Sample Question #9Conditional ProbabilityVerified
  10. SOA Exam P Sample Question #10IndependenceVerified
  11. SOA Exam P Sample Question #11Inclusion–ExclusionVerified
  12. SOA Exam P Sample Question #12Conditional ProbabilityVerified
  13. SOA Exam P Sample Question #14Expected ValueVerified
  14. SOA Exam P Sample Question #16IndependenceVerified
  15. SOA Exam P Sample Question #18Bayes’ TheoremVerified
  16. SOA Exam P Sample Question #19Bayes’ TheoremVerified
  17. SOA Exam P Sample Question #20Bayes’ TheoremVerified
  18. SOA Exam P Sample Question #21Bayes’ TheoremVerified
  19. SOA Exam P Sample Question #22Bayes’ TheoremVerified
  20. SOA Exam P Sample Question #24Bayes’ TheoremVerified
  21. SOA Exam P Sample Question #25Bayes’ TheoremVerified
  22. SOA Exam P Sample Question #26Bayes’ TheoremVerified
  23. SOA Exam P Sample Question #27Bayes’ TheoremVerified
  24. SOA Exam P Sample Question #74Binomial DistributionVerified
  25. SOA Exam P Sample Question #81Conditional ProbabilityVerified
  26. SOA Exam P Sample Question #84Law of Total ProbabilityVerified
  27. SOA Exam P Sample Question #85Discrete DistributionsVerified
  28. SOA Exam P Sample Question #87Set ProbabilityVerified
  29. SOA Exam P Sample Question #90Hypergeometric DistributionVerified
  30. SOA Exam P Sample Question #92Probability ModelingVerified
  31. SOA Exam P Sample Question #94Conditional ExpectationVerified
  32. SOA Exam P Sample Question #97CombinatoricsVerified
  33. SOA Exam P Sample Question #98Expected ValueVerified
  34. SOA Exam P Sample Question #99Set ProbabilityVerified
  35. SOA Exam P Sample Question #100Inclusion-ExclusionVerified
  36. SOA Exam P Sample Question #105Hypergeometric SamplingVerified
  37. SOA Exam P Sample Question #108Geometric-Series ProbabilityVerified
  38. SOA Exam P Sample Question #113Equally Likely Outcome CountingVerified
  39. SOA Exam P Sample Question #120Event IndependenceVerified
  40. SOA Exam P Sample Question #121Mixture ProbabilityVerified
  41. SOA Exam P Sample Question #122Conditional Hypergeometric CountingVerified
  42. SOA Exam P Sample Question #127Bayes RuleVerified
  43. SOA Exam P Sample Question #128Hypergeometric SamplingVerified
  44. SOA Exam P Sample Question #130Inclusion-ExclusionVerified
  45. SOA Exam P Sample Question #132Conditional ProbabilityVerified
  46. SOA Exam P Sample Question #133Bayes' TheoremVerified
  47. SOA Exam P Sample Question #134Discrete Sample SpacesVerified
  48. SOA Exam P Sample Question #135Conditional ProbabilityVerified
  49. SOA Exam P Sample Question #138Conditional Outcome CountingVerified
  50. SOA Exam P Sample Question #147Mutually Exclusive OutcomesVerified
  51. SOA Exam P Sample Question #150Conditional ProbabilityVerified
  52. SOA Exam P Sample Question #151Conditional ProbabilityVerified
  53. SOA Exam P Sample Question #153Events and Set OperationsVerified
  54. SOA Exam P Sample Question #154Law of Total ProbabilityVerified
  55. SOA Exam P Sample Question #156Hypergeometric DistributionVerified
  56. SOA Exam P Sample Question #157Sampling Without ReplacementVerified
  57. SOA Exam P Sample Question #182Set OperationsVerified
  58. SOA Exam P Sample Question #183Set OperationsVerified
  59. SOA Exam P Sample Question #184Inclusion-ExclusionVerified
  60. SOA Exam P Sample Question #185Counting TechniquesVerified
  61. SOA Exam P Sample Question #186Conditional ProbabilityVerified
  62. SOA Exam P Sample Question #187Mixture DistributionsVerified
  63. SOA Exam P Sample Question #188IndependenceVerified
  64. SOA Exam P Sample Question #191Inclusion–ExclusionVerified
  65. SOA Exam P Sample Question #192Mutually Exclusive EventsVerified
  66. SOA Exam P Sample Question #193PermutationsVerified
  67. SOA Exam P Sample Question #194Conditional ProbabilityVerified
  68. SOA Exam P Sample Question #195Conditional ProbabilityVerified
  69. SOA Exam P Sample Question #196Hypergeometric DistributionVerified
  70. SOA Exam P Sample Question #197Sampling Without ReplacementVerified
  71. SOA Exam P Sample Question #198Conditional ProbabilityVerified
  72. SOA Exam P Sample Question #199Conditional ProbabilityVerified
  73. SOA Exam P Sample Question #210IndependenceVerified
  74. SOA Exam P Sample Question #211Geometric DistributionVerified
  75. SOA Exam P Sample Question #233Hypergeometric DistributionVerified
  76. SOA Exam P Sample Question #237Continuous Uniform DistributionVerified
  77. SOA Exam P Sample Question #258Set CountingVerified
  78. SOA Exam P Sample Question #259Conditional ProbabilityVerified
  79. SOA Exam P Sample Question #263IndependenceVerified
  80. SOA Exam P Sample Question #264Bayes' TheoremVerified
  81. SOA Exam P Sample Question #265Law of Total ProbabilityVerified
  82. SOA Exam P Sample Question #274Conditional ProbabilityVerified
  83. SOA Exam P Sample Question #288Conditional ProbabilityVerified
  84. SOA Exam P Sample Question #295IndependenceVerified
  85. SOA Exam P Sample Question #296Contingency TablesVerified
  86. SOA Exam P Sample Question #304Sampling Without ReplacementVerified
  87. SOA Exam P Sample Question #306Bayes' TheoremVerified
  88. SOA Exam P Sample Question #309Bayes' TheoremVerified
  89. SOA Exam P Sample Question #312Conditional ProbabilityVerified
  90. SOA Exam P Sample Question #313IndependenceVerified
  91. SOA Exam P Sample Question #314Bayes' TheoremVerified
  92. SOA Exam P Sample Question #316Bayes' TheoremVerified
  93. SOA Exam P Sample Question #318Bayes' TheoremVerified
  94. SOA Exam P Sample Question #319IndependenceVerified
  95. SOA Exam P Sample Question #323IndependenceVerified
  96. SOA Exam P Sample Question #325Set ProbabilityVerified
  97. SOA Exam P Sample Question #329Bayes' TheoremVerified
  98. SOA Exam P Sample Question #331Set OperationsVerified
  99. SOA Exam P Sample Question #332Counting PrinciplesVerified
  100. SOA Exam P Sample Question #333Hypergeometric DistributionVerified
  101. SOA Exam P Sample Question #334Bayes' TheoremVerified
  102. SOA Exam P Sample Question #335Hypergeometric DistributionVerified
  103. SOA Exam P Sample Question #346Inclusion–ExclusionVerified
  104. SOA Exam P Sample Question #348IndependenceVerified
  105. SOA Exam P Sample Question #349Law of Total ProbabilityVerified
  106. SOA Exam P Sample Question #351IndependenceVerified
  107. SOA Exam P Sample Question #354Conditional ProbabilityVerified
  108. SOA Exam P Sample Question #359Bayes' TheoremVerified
  109. SOA Exam P Sample Question #360Discrete Random VariablesVerified
  110. SOA Exam P Sample Question #363Law of Total ProbabilityVerified
  111. SOA Exam P Sample Question #365Conditional ProbabilityVerified
  112. SOA Exam P Sample Question #366Hypergeometric DistributionVerified
  113. SOA Exam P Sample Question #367Inclusion–ExclusionVerified
  114. SOA Exam P Sample Question #368Inclusion–ExclusionVerified
  115. SOA Exam P Sample Question #369IndependenceVerified
  116. SOA Exam P Sample Question #370Law of Total ProbabilityVerified
  117. SOA Exam P Sample Question #376Hypergeometric DistributionVerified
  118. SOA Exam P Sample Question #377Conditional ProbabilityVerified
  119. SOA Exam P Sample Question #387Conditional ProbabilityVerified
  120. SOA Exam P Sample Question #389Counting MethodsVerified
  121. SOA Exam P Sample Question #398Bayes TheoremVerified
  122. SOA Exam P Sample Question #399Multinomial DistributionVerified
  123. SOA Exam P Sample Question #403Counting MethodsVerified
  124. SOA Exam P Sample Question #405Expected ValueVerified
  125. SOA Exam P Sample Question #408Conditional ProbabilityVerified
  126. SOA Exam P Sample Question #414Combinatorial ProbabilityVerified
  127. SOA Exam P Sample Question #415Inclusion-ExclusionVerified
  128. SOA Exam P Sample Question #418Conditional ProbabilityVerified
  129. SOA Exam P Sample Question #422Mutually Exclusive EventsVerified
  130. SOA Exam P Sample Question #423Conditional ProbabilityVerified
  131. SOA Exam P Sample Question #424Counting MethodsVerified
  132. SOA Exam P Sample Question #437Discrete Random VariablesVerified
  133. SOA Exam P Sample Question #438Hypergeometric DistributionVerified
  134. SOA Exam P Sample Question #445Set ProbabilityVerified
  135. SOA Exam P Sample Question #455Conditional ProbabilityVerified
  136. SOA Exam P Sample Question #456Hypergeometric DistributionVerified
  137. SOA Exam P Sample Question #460Conditional ProbabilityVerified
  138. SOA Exam P Sample Question #468Conditional ProbabilityVerified
  139. SOA Exam P Sample Question #472Binomial DistributionVerified
  140. SOA Exam P Sample Question #486IndependenceVerified
  141. SOA Exam P Sample Question #487Conditional ProbabilityVerified
  142. SOA Exam P Sample Question #490Conditional ProbabilityVerified
  143. SOA Exam P Sample Question #493Conditional ProbabilityVerified
  144. SOA Exam P Sample Question #498Conditional ProbabilityVerified
  145. SOA Exam P Sample Question #500IndependenceVerified
  146. SOA Exam P Sample Question #501Conditional ProbabilityVerified
  147. SOA Exam P Sample Question #506Conditional ProbabilityVerified
  148. SOA Exam P Sample Question #524Combinatorial ProbabilityVerified
  149. SOA Exam P Sample Question #528Conditional ProbabilityVerified
  150. SOA Exam P Sample Question #530Law of Total ProbabilityVerified
  151. SOA Exam P Sample Question #531IndependenceVerified
  152. SOA Exam P Sample Question #532Conditional ProbabilityVerified
  153. SOA Exam P Sample Question #533Conditional ProbabilityVerified
  154. SOA Exam P Sample Question #536Set ProbabilityVerified
  155. SOA Exam P Sample Question #537Conditional ProbabilityVerified
  156. SOA Exam P Sample Question #540Bayes TheoremVerified
  157. SOA Exam P Sample Question #544Conditional ProbabilityVerified
  158. SOA Exam P Sample Question #546Bayes' TheoremVerified
  159. SOA Exam P Sample Question #547Bayes' TheoremVerified
  160. SOA Exam P Sample Question #548Sampling Without ReplacementVerified
  161. SOA Exam P Sample Question #549Combinatorial ProbabilityVerified
  162. SOA Exam P Sample Question #550Combinatorial ProbabilityVerified
  163. SOA Exam P Sample Question #561Combinatorial ProbabilityVerified
  164. SOA Exam P Sample Question #570Counting MethodsVerified
  165. SOA Exam P Sample Question #572Bayes' TheoremVerified
  166. SOA Exam P Sample Question #590Geometric DistributionVerified
  167. SOA Exam P Sample Question #594Sampling Without ReplacementVerified
  168. SOA Exam P Sample Question #602Discrete Random VariablesVerified
  169. SOA Exam P Sample Question #603Bayes' TheoremVerified
  170. SOA Exam P Sample Question #605Bayes' TheoremVerified
  171. SOA Exam P Sample Question #607Disjoint EventsVerified
  172. SOA Exam P Sample Question #620IndependenceVerified
  173. SOA Exam P Sample Question #640Conditional ProbabilityVerified
  174. SOA Exam P Sample Question #641Conditional ProbabilityVerified
  175. SOA Exam P Sample Question #644Conditional ProbabilityVerified
  176. SOA Exam P Sample Question #645Conditional ProbabilityVerified
  177. SOA Exam P Sample Question #646Complement RuleVerified
  178. SOA Exam P Sample Question #647Law of Total ProbabilityVerified
  179. SOA Exam P Sample Question #653IndependenceVerified
  180. SOA Exam P Sample Question #657Inclusion–ExclusionVerified
  181. SOA Exam P Sample Question #658Conditional ProbabilityVerified
  182. SOA Exam P Sample Question #663Conditional ProbabilityVerified
  183. SOA Exam P Sample Question #682Conditional ProbabilityVerified
  184. SOA Exam P Sample Question #683Conditional ProbabilityVerified
  185. SOA Exam P Sample Question #685Conditional ProbabilityVerified
  186. SOA Exam P Sample Question #688Counting MethodsVerified
  187. SOA Exam P Sample Question #691Set ProbabilityVerified
  188. SOA Exam P Sample Question #694Hypergeometric DistributionVerified
  189. SOA Exam P Sample Question #699Bayes' TheoremVerified
  190. SOA Exam P Sample Question #701Discrete Random VariablesVerified
  191. SOA Exam P Sample Question #723Law of Total ProbabilityVerified
  192. SOA Exam P Sample Question #733Conditional ProbabilityVerified

Drill one method at a time

Techniques that keep appearing in General Probability

Each guide collects the questions above that turn on the same method, with the formulas and the errors that cost marks.

57 worked solutions

Exam P Variance problems

Second moments, transformations, sums, covariance terms, and conditional variance decompositions.

55 worked solutions

Exam P Independence problems

Event independence, factorization, independent trials, and the consequences independence does—and does not—justify.

Study the whole topic offline

Every Exam P sample question in one searchable PDF

The 192 pages above stay free. The manual collects the complete Exam P sample set in syllabus order, with the same working, the wrong-choice notes, and one new practice problem per question.